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The corporation's Newsnight programme revealed details of John Whittingdale's relationship with the woman on Tuesday after four newspapers had declined to run the story amid concerns about breaching his privacy.

Labour and privacy campaigners demanded that Mr Whittingdale be stripped of his role over press regulation, suggesting that newspapers had held the threat of publication against the Culture Secretary.

Mr Whittingdale with a female companion in 2013Credit:
FameFlynet

However last night a Cabinet Minister questioned the BBC's motive for broadcasting the story and accused it of targeting Mr Whittingdale over his role in deciding on the future of the licence fee.

The Telegraph understands that BBC executives had argued with Mr Whittingdale just last week over his plans to hand a chunk of the licence fee to commercial rivals to spend on children's programming.

A Cabinet minister told The Telegraph: "The way the BBC has marched into a story that should be an entirely private matter and is hardly in the public interest suggest that they have got an agenda in attacking John. His reputation is being smeared.

"It is really not the way we expect a major public service broadcaster to behave. People will conclude that it's all about licence fee. Hacked Off purport to be the champions of privacy but are quite happy to discard somebody else's privacy. John has been smeared over this."

Andrew Bridgen, a Conservative MP, said: "The BBC have a vested interest in having John Whittingdale replaced with a more sympathetic secretary of state.

"They are the place where the vast majority of the public get their news, so they have the power to decide what is news and what isn't. I am surprised that they think this is the story they should lead on all day."

Hacked Off, a group that has campaigned against press invasions of privacy, was also accused of "unbelievable hypocrisy" after using the revelation to claim that newspapers had suppressed the story due to Mr Whittingdale's role overseeing press regulation.

Mr Whittingdale with a female companion in 2013Credit:
FameFlynet

The revelations left Labour divided after three members of the shadow cabinet refused to back the party's call for Mr Whittingdale to be barred from overseeing press standards.

Labour's deputy leader Tom Watson said that he had actually suggested to one newspaper that it would be breaching Mr Whittingdale's privacy to run the story.

But yesterday other members of the Labour party appeared to argue that there was a public interest in the story.

There is no suggestion that Mr Whittingdale knew the woman was a prostitute before he was approached by a tabloid newspaper over the allegations.

A senior BBC source said that claims that the corporation broadcast the story were linked to the row over the future of the licence fee were "clearly nonsense", while a Newsnight spokesman said that there was a "clear public interest" in the revelations.

Mr Whittingdale's relationship with the sex worker he had met through online dating was made public by Newsnight on Tuesday during an interview with Brian Cathcart, the founder of Hacked Off.

Unbelievable hypocrisy from @labour on @JWhittingdale. The fact papers didn't run story in first place shows press regulation is working

The Culture Secretary issued a statement admitting that he had been in a relationship with the woman, whom he met on the dating website Match.com, between August 2013 and February 2014.

However Mr Whittingdale, who is divorced, said he did not know that she was a "dominatrix" and broke off the relationship when he discovered that she was a sex worker. The relationship took place before he became the Culture Secretary.

Four newspapers are said to have been aware of the relationship but decided not to publish amid concerns that the story was not in the public interest and could be a breach of his privacy.

However Hacked Off claimed that the newspapers had an "obligation" to run it and claimed that Mr Whittingdale had been "compromised" and should "get out of the way".

Jeremy Corbyn called for Mr Whittingdale to withdraw from decisions on press regulation to "allay any concerns about perceptions of any undue influence".

However he was contradicted by Hilary Benn, the shadow foreign secretary, said that Mr Whittingdale's relationship was "private" and was "nobody else's business". "He ought to get on and do his job," he said.

Tom Watson, Labour's Deputy Leader, also disclosed that he had been contacted by a newspaper but had urged them not to publish the story.

He said: “I was very clear that he had a right to privacy and that as far as I could see there was no public interest in the story, although it was not for me to decide.”

Diane Abbott, the shadow international development secretary, also said that Mr Whittingdale's relationship was a "private" matter.

Liam Fox, the Conservative former defence secretary, accused Labour of “unbelievable hypocrisy”, adding: “The fact papers didn't run story in first place shows press regulation is working.”

Kate Hoey, the Labour MP, also said that Hacked Off were hypocrites. She said: “I thought Hacked Off wanted less press intrusion or is that only for celebrity actors."

Mr Whittingdale faced questions from the BBC about his relationship as he pressed for the return of so-called ‘top-slicing’ of the licence fee.

Officials have suggested it could create a pot of cash for producers to bid for amid concerns independent children’s programming is struggling to survive while the BBC dominates.

Sources close to the situation said the plans provoked outrage from the BBC, which believed it had successfully fought off efforts to loosen its grip on the licence fee when it struck a funding deal with George Osborne last year.

A spokesperson for Newsnight said: "There is a clear public interest in establishing whether John Whittingdale's ability to oversee press regulation without fear or favour has been compromised by the fact that four newspaper groups knew about the story which would be highly embarrassing to him if published.

“The story was already being reported online and in a magazine - Newsnight ran the story after securing an on-the-record statement from the Minister confirming his relationship with a sex worker and addressing the allegation that this created at least the appearance of a conflict of interest."

A senior BBC source said: "BBC News made the decision to run this story, and no one else. The director-general was not asked to approve the story in any way, and was told that Newsnight was due to publish the story shortly before the programme.

"The issue of topslicing, and the Newsnight story are in no way related. The notion that annoying the government and Fleet Street at the same time is somehow helpful for the charter process is clearly nonsense."

The BBC said it had not received a complaint from Mr Whittingdale over the story. A senior BBC source said: "Our journalists make their own judgements, based on the merits of individual stories. The notion that there is any ulterior motive is totally risible and absolutely unsupported by the facts."